We follow the DDPM [1]} definition of diffusion as a Markov noising process with latents \(\lbrace \mathbf {z}_t\rbrace _{t=0}^T\)  that follow a forward noising process \(q(\mathbf {z}_t | \mathbf {x})\) , where \(\mathbf {x} \sim p(\mathbf {x})\)  is drawn from the data distribution.
The forward noising process is defined as
\( {q(\mathbf {z}_{t} | \mathbf {x}) \sim \mathcal {N}(\sqrt{\bar{\alpha }_{t}}\mathbf {x}, (1 - \bar{\alpha }_{t})\mathbf {I}),}\) 
